Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8114)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8114.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 1/4}, z] == (1/331776000) ((4 (41472000 + 82944000 Sqrt[z] - 12488175 z + 182414700 z^(3/2) - 13487040 z^2 + 157317120 z^(5/2) + 46609920 z^3 - 198297600 z^(7/2) - 4177920 z^4 + 16908288 z^(9/2) + 65536 z^5 - 262144 z^(11/2) + E^(4 Sqrt[z]) (41472000 - 82944000 Sqrt[z] - 12488175 z - 182414700 z^(3/2) - 13487040 z^2 - 157317120 z^(5/2) + 46609920 z^3 + 198297600 z^(7/2) - 4177920 z^4 - 16908288 z^(9/2) + 65536 z^5 + 262144 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (476974575 + 778734000 z + 755136000 z^2 - 805478400 z^3 + 67829760 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (476974575 + 778734000 z + 755136000 z^2 - 805478400 z^3 + 67829760 z^4 - 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 755136000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 778734000 </cn> <ci> z </ci> </apply> <cn type='integer'> 476974575 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]